I am able to reproduce all the three mentioned issues on a PC+Linux
platform with a NetBeans 3.6 beta. They will not be fixed in NetBeans 3.6.
Issue #1 is caused by bug #40507 ("Activating a TopComponent does not
move focus to its focus cycle").

issue 1: fixed - the focus is moved into the editor by now.
issue 2: fixed - Remove Property button is disabled when no
property is selected (for example when there is no property).
issue 3: this seems to be a misunderstanding. It works correctly.
The only "problem" is that (on some look and feels?) Ctrl+Tab
moves focus on the scrollbar of the textarea. After that just
simple Tab must be used to move focus to the next component.